Global Well-Posedness and Large-Time Behavior of 1D Compressible Navier-Stokes System with Density-Depending Viscosity and Vacuum in Unbounded Domains

2018/08/23 by Li, Kexin, Lü, Boqiang, Wang, Yixuan
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.07649

Abstract

We consider the Cauchy problem for one-dimensional (1D) barotropic compressible Navier-Stokes equations with density-dependent viscosity and large external force. Under a general assumption on the density-dependent viscosity, we prove that the Cauchy problem admits a unique global strong (classical) solution for the large initial data with vacuum. Moreover, the density is proved to be bounded from above time-independently. As a consequence, we obtain the large time behavior of the solution without external forces.

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